A Novel Multiple Imputation Approach For Parameter Estimation in Observation-Driven Time Series Models With Missing Data
Guilherme Pumi, Taiane Schaedler Prass, Douglas Krauthein Verdum
TL;DR
This work tackles missing data in time series within the framework of Observation-Driven Models (ODM) by introducing a novel multiple-imputation approach that preserves the underlying dependence structure. Given an initial parameter estimate, missing values are imputed by reconstructing the conditional systematic component and sampling from $f(\cdot|\hat{\mu}_t,\hat{\boldsymbol{\nu}}_0;\mathscr{F}_{t-1})$ with $\hat{\mu}_t=g^{-1}(A(\boldsymbol{X}_t,\cdot;\hat{\boldsymbol{\lambda}}_0))$, producing complete series on which estimators are re-estimated and iterated until convergence. The method is applicable to continuous, discrete, and mixed data and is compatible with any estimator in ODMs, with two stopping criteria (CVSC and VRSC) and a practical strategy for non-convergence. Through a comprehensive Monte Carlo study on GARMA-type models with up to $70\%$ missing data and an empirical application to energy-storage data, the approach demonstrates improved preservation of variance and dependence properties and provides practical guidance for convergence and computation. Overall, the proposed MI framework offers robust parameter estimation under missing data in ODMs, broadening applicability in econometrics and energy-system modeling.
Abstract
Handling missing data in time series is a complex problem due to the presence of temporal dependence. General-purpose imputation methods, while widely used, often distort key statistical properties of the data, such as variance and dependence structure, leading to biased estimation and misleading inference. These issues become more pronounced in models that explicitly rely on capturing serial dependence, as standard imputation techniques fail to preserve the underlying dynamics. This paper proposes a novel multiple imputation method specifically designed for parameter estimation in observation-driven models (ODM). The approach takes advantage of the iterative nature of the systematic component in ODM to propagate the dependence structure through missing data, minimizing its impact on estimation. Unlike traditional imputation techniques, the proposed method accommodates continuous, discrete, and mixed-type data while preserving key distributional and dependence properties. We evaluate its performance through Monte Carlo simulations in the context of GARMA models, considering time series with up to 70\% missing data. An application to the proportion of stocked energy stored in South Brazil further demonstrates its practical utility.